The city’s teachers pension plan is under-funded by as much as $36 billion — more than twice the current estimates of that gap, according to an alarming new report.

While in much better shape, the State’s retirement system could be as much as $25 billion short of the funding needed to fulfill its pay-out promises.

Overall, a new Manhattan Institute study found that teacher pension systems across the nation are under-funded by $484 billion because they’re overestimating the returns on their investments.

That money is guaranteed by taxpayers — through tax hikes or cuts in services — no matter how the funds ultimately perform.

The failure of pension systems to account for the recent stock market plunge in their balances boosts the funding shortfall by an additional $116 billion, the study says.

Adding both of the shortfalls to the current funding gap estimate of $332 billion puts the country’s pension plans at a whopping $933 billion in the hole.

“States need to recognize how expensive this problem is that they’ve created,” said Josh Barro, a senior fellow at the Manhattan Institute, a conservative think tank. “We think that states need to do what’s been done in the private sector and start moving employees to defined-contribution plans, like 401Ks.”

Barro said the crux of the problem is that most public pension plans — including New York’s — guarantee a hefty 8 percent return on their investments.

By contrast, most private pension funds anticipate a more reasonable return of 6 percent, the study says.

Applying the more conservative estimate of returns — and factoring in the recent stock market losses — shows just 46 percent of the city’s pension plan to be funded.

The average across the 59 city and state pension plans studied was a 54 percent funding rate — with New York State’s ranking fourth overall, at 77 percent.

While Barro applauded recent changes to the city’s teachers pension plan, he said its relief was still a long way off.

Those changes — which created a new Tier V category for entering teachers — doubled vesting time to 10 years, raised the retirement age to 62, and extended annual employee contributions through their retirement.